This invention relates to the field of frequency measurement and analysis, and more particularly to the field of accurately measuring the frequency of individual spectral lines from the responses of two filters, or from the response of one filter as the spectral line is moved with respect to that filter's center frequency by a sweeping local oscillator.
A spectrum analyzer is an electronic instrument for providing a frequency domain view of an electrical signal, i.e., how the energy of the signal is distributed in terms of frequency. Many spectrum analyzers, both digital and analog, rely on banks of filters to determine the amount of energy occurring at different frequencies. In an analog spectrum analyzer, a number of physical filters tuned to different frequencies each respond to an input signal that may be shifted in frequency by mixing with a local oscillator.
Digital spectrum analyzers can apply the same principle using digital filters instead of analog ones. These analyzers first sample and digitize the activity of the signal under analysis to produce a series of time domain digitized samples. The sampling rate must be at least twice as high as the bandwidth of interest. Those time domain samples are then applied to a bank of digital band pass filters tuned to different frequencies to cover the frequency band of the input signal. The output of those filters can be sampled (simultaneously) at a rate proportional to their bandwidth, to avoid aliasing.
Generally, one of several variations of the Discrete Fourier Transform (DFT), usually the Fast Fourier Transform (FFT), is used to build the bank of filters. These methods are described in detail in "Digital Signal Processing" by Oppenheim and Schafer (Prentice-Hall, Inc. 1975), which is hereby incorporated by reference, in "Multirate Digital Signal Processing" by Crochiere and Rabiner (Prentice-Hall, 1983), which is also hereby incorporated by reference, and many other books and papers.
As explained in Chapter 7 of "Multirate Digital Signal Processing" by Crochiere and Rabiner (Prentice-Hall, 1983), there are methods available that allow the time record length, M, and the number of output filter bins, K, to be different. The "polyphase structure" approach allows M to be any integer multiple of K. The "weighted overlap-add structures" approach removes that constraint, permitting M to be larger than K without being an integer multiple of it. However, using the longer time records required for a larger M is computationally expensive, adding to the time and/or compute resources required for each complete DFT calculation.
The shape of each of the output filters, i.e. its frequency response, and hence its impulse response, is independent of the number of filters. The number of samples in the time record and the number of output bins or filters are selectable, and may differ from each other, but the implementation of the FFT algorithm requires that the number of filters to be equal to the radix of the FFT raised to the power of an integer number.
If separate individual, but identical, filters are used to cover a given analysis span with Fs/K frequency resolution, K individual filters with incrementally adjusted center frequencies are necessary to create a filter bank covering that span. If additional analysis spans are desired, additional corresponding filter banks are necessary. This multiplicity of hardware rapidly becomes prohibitive.
However, if the available hardware is fast enough, it is possible to build fewer filters, for example, m filters, where m&lt;K. This can be done by time sharing the hardware between the lesser number of filters to achieve the K required filters. This time sharing approach can be implemented in either of two ways. Either the hardware for a single band pass filter can be shared between K/m filters by changing the center frequency of the hardware. Or, the hardware of a single low pass filter can be shared between K/m filters by demodulating the input signal by different frequencies, each of which corresponds to the desired filter center frequencies. These demodulated signals are then put through the single low pass filter and then remodulated back up by the same amount that they were demodulated previously.
Both of these approaches are equivalent. However, in one case, the filter is moved with respect to the signal, while in the other case, the signal is moved with respect to the filter. FIG. 1 illustrates the hardware equivalent of the latter approach.
By performing this demodulation, remodulation process in rapid sequence for incremented center frequencies, a single hardware realized filter can be time-shared into a bank of equally spaced filters. To do this it is necessary to sample the output at a rate of r*Fs/K, where Fs is the sampling frequency of the input signal, r is a constant that depends on the filter shape, and K is the number of filter increments across the desired analysis span. The relationship between Fs and the frequency span is determined by the Nyquist theorem.
The relationship of K and M can be modified to be M=Q*K where Q is an integer. M can always be made to satisfy this relationship by adding "0" terms. This separation of K and M permits any filter shape to be realized, at least theoretically.
A wide variety of filter shapes have also been employed by the designers of analog spectrum analyzers. One of the filter shapes used in analog spectrum analyzers and in radars is a Gaussian filter shape (equation 1). ##EQU1##
where .sigma..sub.f is one standard deviation measured in frequency,
f.sub.c is the center frequency, and
f.sub.x is any frequency of interest.
These filters have traditionally been valued for several of their characteristics, including their signal extraction abilities and transient response functions. For example, U.S. Pat. No. 3,774,201 to Collins for a "Time Compression Signal Processor" teaches, at column 13, lines 14-19, "Filters with more nearly rectangular characteristic curves would be better suited for straight forward spectrum analysis, but part of the problem in a radar system is extracting the signal from a noisy background; Gaussian filters were better at extracting the signal."
U.S. Pat. No. 4,610,540 to Mossey for a "Frequency Burst Analyzer", hereby incorporated by reference, shows multiple filters being used to interpolate the location of signals between the center frequencies of the filters. At column 5, lines 7-62, of this Mossey patent, three methods of interpolating the location of a signal are described, collectively referred to as alternative means of "regression analysis". All of the methods taught by Mossey are somewhat complex and computationally time consuming, as well as requiring the output of as many as four filters to accurately determine the result.
What is desired is a method and apparatus for determining the location of a spectral line between the center frequencies of two adjacent filters, or one filter if the signal is moved with respect to its center frequency, that is fast and accurate and is suitable for use in digital as well as analog spectrum analyzers.